Vor.vMx 4, NvMsxR 10 P HYSI CAI. RKVI K%' I.KTTKRS Mar 15, 1960

The line shape therefore should consist of maxi-ma corresponding to the transitions between Lan-dau levels. The exciton line shape is also simi-lar and is hence favorable for accurate deter-mination of the various parameters. The excitonZeeman pattern should give discrete resolvablelines for all crystal directions and allow themeasurement of the anisotropic g factors. Thispattern in the [110]plane will have three branchesdue to the spin alone.

The above transition should be extremely at-tractive for use in an optically excited cyclotronresonance maser since the fundamental excita-tion is in a very desirable range of the opticalspectrum where pulsed line sources of. the orderof several watts or more are possible. Further-more, this transition fulfills the necessary re-quirements for such a maser. " The direct tran-sition permits selective excitation to discretemagnetic levels deep into the bands allowing po-pulation inversion of holes or electrons relativeto Landau levels of lower quantum number. Dueto the interaction of the spin-orbit split L„va-lence bands, these should have large change ofcurvature. This will permit unequally spacedmagnetic levels so that selective transitionsdownward in energy between only two unique le-vels can be chosen by the resonant radiation inan interferometer tuned to this frequency. Thusthe induced electric dipole cyclotron resonancetransition will be emissive. . From the valuesestimated in this paper for H along a [ill] direc-tion, with fields of the order of 4&10' gauss or

larger which are available and desired for theinterband transitions, the maser should be oper-able in the submillimeter or far infrared regionat approximately 600 microns.

The author is grateful to Dr. Laura Both forseveral suggestions and for checking the esti-mates of the effective-mass values. He has alsobenefitted from discussions with Professor Q. F.Koster, Dr. H. J. Zeiger, and Dr. S. Zwerdling.

Operated with support from the U. S. Army, Navy,and Air Force.-

~L. M. Both and B. Lax, Phys. Rev. Letters 3, 217(1959}.

2J. C. Phillips, J. Phys. Chem. Solids 12, 208(1960}

3K. J. Button, L. M. Both, W. H. Kleiner, S.Zwerdling, and B. Lax, Phys. Rev. Letters 2, 161(1959).

46. Feher, D, K. Wilson, and E. A. Gere, Phys.Rev. Letters 3, 25 (1959).

~H. R. Philipp and E. A. Taft, Phys. Rev. 113,1002 (1959).

IL. M. Roth (to be published).~M. Lampert, Phys. Rev. 97, 352 (1955).SS. Zwerdling, B. Lax, L. M. Roth, and K. J.

Button, Phys. Rev. 114, 80 (1959).88,. J. Elliott, J. P. McLean, and O. G. Macfarlane,

Proc. Phys. Soc. (London) 72, 553 (1958).~ L. M. Both, B. Lax, and S. Zwerdling, Phys. Rev.

114, 90 (1959); B. Lax and S. Zwerdling, Progress inSemiconductors (to be published}.

~~B. Lax, Conference on Quantum Electronics-Resonance Phenomena (Columbia University Press,New York, 1960).

DIRECTION OF THE EFFECTIVE MAGNETIC FIELD AT THE NUCLEUS IN FERROMAGNETIC IRONt

S. S. Hanna, J. Heberle, Q. J. Perlow, R. S. Preston, and D. H. VincentArgonne National Laboratory, Argonne, Illinois

(Received April 28, 1960)

In a recent experiment' it was shown that inferromagnetic iron the effective magnetic fieldat the iron nucleus is strongly correlated withthe magnetization. The sense of the correlation,however, was not determined, i.e. , it was notknown whether the effective field was parallel orantiparallel to the magnetization. The sense ofthe correlation has now been established by ob-serving the change in the hyperfine splitting ofthe nuclear energy levels of Fe" on applicationof. an external field of 3.7 to 20 koe.

In an earlier paper' we presented the hyperfine

spectrum obtained in the resonant Mossbauer'absorption in Fe". The interpretation given tothe spectrum has since been confirmed in detail.Several groups have shown the correctness ofthe hyperfine pattern by observing the spectrumwhen different alloys and compounds of iron areused. ' Qossard, Portis, and Sandie' have ob-served the nuclear magnetic resonance in theground state of Fe" at a frequency correspondingto a value of the effective field in close agreementwith the value of 333 koe deduced in reference 2.In addition, Ewan, Graham, and Geiger~ have

5i3

VOLUME 4) NUMBER 10 PHYSICAL RKVI KW LKTTKRS Mxv 15, 1960

found that the E2 admixture in the M1 radiationis less than 10 4, which confirms that the effectof E2 radiation in the spectrum is indeed negli-gible. '

Experimentally it was feasible to apply a largemagnetic field only to the source of the resonantradiation. The absorber was either in the fring-ing field of the electromagnet holding the sourceor in a small parallel magnetic field of its own,applied to produce a definite magnetization in theabsorber. At the top of Fig. 1 is shown the ve-locity spectrum which is applicable if the hyper-fine splittings in source and absorber are identi-cal. The intensities are appropriate to the emis-sion of polarized radiation from the source butto an unpolarized absorption process. If, on theother hand, the hyperfine splittings in the emitterare about 10% greater (for example) than thosein the absorber, then the complex spectrum atthe bottom of Fig. 1 is obtained. It is clear thata study of the singlet line 6 affords the best meansof determining the change that an external fieldproduces in the hyperfine splitting.

For the effective field at the nucleus we write

assumed in Eq. (1) that Hz, is not appreciablyinfluenced by Hext. The quantity of interest isthe sign of H~, . Since M, and Hext are parallelunder saturation conditions, the sign can be de-termined by observing whether the hyperfinesplitting increases or decreases on applicationof a field. With a field of 17.6 koe a shift of+2.65% is expected in line 6.

The experimental technique was similar to thatin our earlier work. '~'~' The carriage of a lathewas used to provide velocities by means of whichthe spectrum was scanned. The source wasmounted in the narrow gap of an electromagnetcapable of producing fields up to 20 koe. Themagnet was attached rigidly to the end of the latheand the absorber was mounted on the carriage.The result obtained for line 6 is shown in Fig. 2.On application of the field to the source, a shiftto lower energy is unmistakable. The correlation

H =H M +Hext, 60

where Mo is a unit, vector along the direction ofmagnetization in a ferromagnetic domain, and

0« is the magnitude of the effective field in theabsence of the external field Hext. The latterquantity includes the demagnetizing field whichis negligible for the planar samples used. SinceHext/II+~«1 in the present experiment, it is

58

5pECD ~

7.6 koe

'It I I ~

2 3 4 IO I I

SPEED (mm/sec)l2

FIG. 1. Theoretical absorption spectra of 14.4-kevresonance radiation from Fe . Top: metallic sourceand absorber with identical hyperfine splittings. Bot-tom: same source and absorber but with the splittingin the source increased by 10 Vo.

FIG. 2. Line 6 observed with Next ——0 and &ext ——17.6koe, where Hext is the external field applied to thesource of resonance radiation. The ordinate is in unitsof 103 counts.

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VOLUME 4, NUMBER 10 P HYSICAI. REVI EW I, ETYERS m~v ~S, ~g60

is therefore negative. The magnitude of the ob-served shift is (2.7 + 0.4) % which is compatiblewith the linear relation H~ =Hz - Hext. A negativeshift of about the correct magnitude was also ob-served in line 4. The multiplet structure in line4 is symmetrical (Fig. l) and so does not seriouslyinterfere with the observation of a shift of itscentral member.

The effective field at the iron nucleus has now

been determined both in sign and magnitude. Theexistence of such a large negative field (-333 koe)was unexpected. Marshall' has discussed a num-ber of sources of the effective nuclear field. Theseconsist mainly of direct effects of the Sd electronsand indirect effects of polarization of the variouss electrons, which then contribute to the field viathe Fermi contact interaction. The polarizationof inner shells of electrons results in negativecontributions to the field. In view of the experi-mental result these negative terms must completelydominate the other contributions.

We are grateful to S. Raboy for loan of the mag-net. We wish also to thank M. R. Perlow for pre-paration of the source; F. J. Karasek for contin-uing to supply us with thin rolled iron foils; and

E. Kowalski for assistance in taking the data. V/'e

have profited from a stimulating discussion with%. Marshall.

This work was performed under the auspices of theU. S. Atomic Energy Commission.

~G. J. Perlow, S. S. Hanna, M. Hamermesh, C.Little]ohn, D. H. Vincent, R. 8. Preston, and J.Heberle, Phys. Rev. Letters 4, 74 (1960).

28. 8. Hanna, J. Heberle, C. Littlejohn, G. J.Perlow, B. S. Preston, and D. H. Vincent, Phys. Bev.Letters 4, 177 (1960).

IB. L. Mossbauer, Z. Physik 151, 124 (1958).4(Ferrocyanide) S. L. Ruby, L. M. Epstein, and

K. H. Sun (to be published);(ferrocyanide, stainlesssteel) G. K. Wertheim, Phys. Rev. Letters 4, 409(1960); (Fe20~) O. C. Kistner and A. W. Sunyar, Phys.Rev. Letters 4, 412 (1960).

5A. C. Gossard, A. M. Portis, and W. J. Sandie(to be published) .

86. T. Ewan, R. L. Graham, and J. S. Geiger (tobe published) .

~8. S. Hanna, J. Heberle, C. Little]ohn, G. J.Perlow, B. S. Preston, and D. H. Vincent, Phys. Bev.Letters 4, 28 (1960).

SW. . Marshall, Phys. Bev. 110, 1280 (1958), andprivate communication.

RESONANCES IN C ON CARBON REACTIONS

E. Almqvist, D. A. Bromley, and J. A. KuehnerAtomic Energy of Canada Limited, Chalk River Laboratories, Chalk River, Ontario, Canada

(Received March 28, 1960)

The reaction yield from C ' on carbon in thelaboratory energy range 9-29 Mev has been in-vestigated using C" beams of precisely definedenergy from the Chalk River tandem accelerator.The measured excitation curves for all reactionproducts studied reveal unexpected, sharp, iso-lated resonances at incident energies just belowthe Coulomb barrier corresponding to excitationsin Mg" =20 Mev. At higher energies where stronginterference structure was previously observedin the elastic scattering, ' the reaction resonancestructure is considerably less marked. In con-trast to these results for the C"+ C system,similar measurements for 0" ions on oxygentargets show no such resonant behavior; in thiscase the incident energy required to reach thetop of the Coulomb barrier is somewhat higherand corresponds to 27-Mev excitation in S". Itis noted that both reactions are restricted toonly those states allowed to a system of two

identical spin-zero Bosons.The various excitation curves for C ' on car-

bon in Fig. 1 show marked similarity; particular-ly for incident energies below 6.5 Mev (center-of-mass system), sharp resonances appear inall curves at energies of 5.68 Mev, 6.00 Mev,and 6.32 Mev. The observed widths of thesepeaks are equal to the energy loss in the 40-pg jcm' carbon targets. This amounts to 100 kevin the c.m. system; consequently, in each casethe true resonance width is almost certainlyless than this. Additional measurements notshown in the figures on alpha particles detected'at 2V and 62' and protons detected' at 62 in thelaboratory and on all gamma radiation of energygreater than 2.8 Mev also show these same sharpresonances below the Coulomb barrier. Thefact that these resonance peaks appear at theidentical incident energies for all reaction prod-ucts independently of the angle of observation

515